Author: Pedro J. Aphalo
Date: 2025-10-02

# User Guide

### Package ‘photobiologyPlants’ 0.6.1.1

#### Pedro J. Aphalo

#### 2025-10-02

## Introduction

This package provides data sets and functions relevant to the photobiology of plants. It is part of a suite, which has package ‘photobiology’ at its core. Please visit (http://www.r4photobiology.info/) for more details. For more details on plotting spectra, please consult the documentation for package ‘ggspectra’, and for information on the calculation of summaries and maths operations between spectra, please, consult the documentation for package ‘photobiology’.

See the User Guide for packages ‘photobiology’ and ‘ggspectra’ for instructions on how to work with spectral data. As package ‘ggspectra’ is only suggested, in this vignette it is loaded an used conditionally on its availability.

    library(photobiology)
    library(photobiologyPlants)
    library(photobiologyWavebands)
    eval_plots <- requireNamespace("ggspectra", quietly = TRUE)
    if (eval_plots) library(ggspectra)

    theme_set(theme_bw())

## Photon ratios relevant to plants

`R_FR()` and other functions for computing photon ratios are convenience functions implemented using function `q_ratio()` and `q_irrad()` from package ‘photobiology’ and waveband definitions from package ‘photobiologyWavebands’ with defaults arguments to parameter `std` for wavelength ranges commonly used in the field of plant photobiology. These functions can be used with one or more spectra as argument.

    R_FR(sun.spct)

    ## R:FR[q:q]
    ##  1.242474
    ## attr(,"radiation.unit")
    ## [1] "q:q ratio"

Here, the argument named `attr2tb` is forwarded to method `q_ratio` from package ‘photobiology’ to copy metadata from the spectra into the returned data frame.

    R_FR(sun_evening.spct,
         std = "Smith20",
         attr2tb = c("when.measured" = "time.UTC", "lat" = "latitude"))

    ## # A tibble: 5 × 4
    ##   spct.idx `R:FR[q:q]` time.UTC            latitude
    ##   <fct>          <dbl> <dttm>                 <dbl>
    ## 1 time.01         1.18 2023-06-12 18:38:00     60.2
    ## 2 time.02         1.19 2023-06-12 18:39:00     60.2
    ## 3 time.03         1.18 2023-06-12 18:40:00     60.2
    ## 4 time.04         1.16 2023-06-12 18:41:00     60.2
    ## 5 time.05         1.12 2023-06-12 18:42:00     60.2

## Calculating the phytochrome photoequilibrium

In the examples below we use the solar spectral data included in package ‘photobiology’ as a data frame in object `sun.spct`.

We can calculate the phytochrome photoequilibrium from spectral irradiance data contained in a `source_spct` object as follows.

    Pfr_Ptot(sun.spct)

    ## [1] 0.68341

We can also calcualte the red:far-red photon ratio, in this second example, for the same spectrum as above

    R_FR(sun.spct)

    ## R:FR[q:q]
    ##  1.242474
    ## attr(,"radiation.unit")
    ## [1] "q:q ratio"

which is equivalent to calculating it using package ‘photobiology’ directly

    q_ratio(sun.spct, Red("Smith10"), Far_red("Smith10"))

    ## R:FR[q:q]
    ##  1.266704
    ## attr(,"radiation.unit")
    ## [1] "q:q ratio"

We can, and should whenever spectral data are available, calculate the photoequilibrium as above, directly from these data. It is possible to obtain and approximation in case of the solar spectrum and other broad spectra, using the red:far-red photon ratio. The calculation, however, is only strictly valid, for di-chromatic illumination with red plus far-red light.

    Pfr_Ptot_R_FR(R_FR(sun.spct))

    ## R:FR[q:q]
    ## 0.7025925

Here we calculated the R:FR ratio from spectral data, but in practice one would use this function only when spectral data is not available as when a R plus FR sensor is used. We can see that in such a case the photoequilibrium calculated is only a rough approximation. For sunlight, in the example above when using spectral data we obtained a value of 0.683 in contrast to 0.703 when using the R:FR photon ratio. For other light sources differences can be much larger. Furthermore, here we used the true R:FR ratio calculated from the spectrum, while broad-band red:far-red sensors guive only an approximation, which is good for sunlight, but which will be innacurate for artifical light, unless a special calibration is done for each type of lamp.

In the case of monochromatic light we can still use the same functions, as the defaults are such that we can use a single value as the ‘w.length’ argument, to obtain the Pfr:P ratio. For monochromatic light, irradiance is irrelevant for the photoequilibrium (steady-state).

    Pfr_Ptot(660)

    ## [1] 0.869649

    Pfr_Ptot(735)

    ## [1] 0.01749967

    Pfr_Ptot(c(660, 735))

    ## [1] 0.86964902 0.01749967

    Pfr_Ptot(435)

    ## [1] 0.3859998

We can also plot Pfr:Ptot as a function of wavelength (nm) of monochromatic light. The default is to return a vector for short input vectors, and a `response_spct` object otherwise, but this can be changed through argument `spct.out`.

    autoplot(Pfr_Ptot(300:770), unit.out = "photon",
             w.band = Plant_bands(),
             annotations = c("colour.guide", "labels", "boxes")) +
      labs(y = "Phytochrome photoequilibrium, Pfr:Ptot ratio")

It is, of course, also possible to use base R plotting functions, or as shown here functions from package ‘ggplot2’

    ggplot(data = Pfr_Ptot(300:770), aes(w.length, s.q.response)) +
      geom_line() +
      labs(x = "Wavelength (nm)",
           y = "Phytochrome photoequilibrium, Pfr:Ptot ratio")

In the case of dichromatic illumination with red (660 nm) and far-red (730 nm) light, we can use a different function that takes the R:FR photon ratio as argument.

These computations are valid only for true mixes of light at these two wavelengths but not valid for broad spectra like sunlight and especially inaccurate for plant growth lamps with peaks in their output spectrum, such as most discharge lamps (sodium, mercury, multi-metal, fluorescent tubes) and many LED lamps.

    Pfr_Ptot_R_FR(1.15)

    ## [1] 0.6919699

    Pfr_Ptot_R_FR(0.01)

    ## [1] 0.04747996

    Pfr_Ptot_R_FR(c(1.15,0.01))

    ## [1] 0.69196990 0.04747996

It is also easy to plot Pfr:P ratio as a function of R:FR photon ratio. However we have to remember that such values are exact only for dichromatic light, and only a very rough approximation for wide-spectrum light sources. For wide-spectrum light sources, the photoequilibrium should, if possible, be calculated from spectral irradiance data.

    ex6.data <- data.frame(r.fr=seq(0.01, 5.0, length.out=100), Pfr.p=numeric(100))
    ex6.data$Pfr.p <- Pfr_Ptot_R_FR(ex6.data$r.fr)
    ggplot(data=ex6.data, aes(r.fr, Pfr.p)) +
      geom_line() +
        labs(x ="R:FR photon ratio",
             y = "Phytochrome photoequilibrium, Pfr:Ptot ratio")

## Calculating reaction rates

    with(clip_wl(sun.spct, c(300,770)), Phy_reaction_rates(w.length, s.e.irrad))

    ## $k1
    ## [1] 1.25935
    ##
    ## $k2
    ## [1] 0.5833947
    ##
    ## $nu
    ## [1] 1.842745

## Calculating the absorption cross section at given wavelengths

The phytochrome photoequilibrium cannot be calculated from the absorptance spectra of Pr and Pfr, because Pr and Pfr have different quantum yields for the respective phototransformations. We need to use action spectra, which in this context are usually called `absorption cross-sections'. They can be calculated as the product of absorptance and quantum yield. The values in these spectra, in the case of Phy are called`Sigma’.

Here we reproduce Figure 3 in Mancinelli (1994), which gives the ‘Relative photoconversion cross-sections’ of Pr (\(\sigma_R\)) and Pfr (\(\sigma_{FR}\)). The values are expressed relative to \(\sigma_R\) at its maximum at \(\lambda = 666\) nm.

    ex7.data <- data.frame(w.length=seq(300, 770, length.out=100))
    ex7.data$sigma.r <- Phy_Sigma_R(ex7.data$w.length)
    ex7.data$sigma.fr <- Phy_Sigma_FR(ex7.data$w.length)
    ex7.data$sigma <- Phy_Sigma(ex7.data$w.length)
    ggplot(ex7.data, aes(x = w.length)) +
      geom_line(aes(y = sigma.r/ max(sigma.r)), colour = "red") +
      geom_line(aes(y = sigma.fr/ max(sigma.r))) +
      labs(x = "Wavelength (nm)", y = expression(sigma[R]~"and"~sigma[FR]))

    rm(ex7.data)

## Spectral absorbance of cryptochromes

    names(CRYs.mspct)

    ## [1] "CRY1_dark"  "CRY1_light" "CRY2_dark"  "CRY2_light" "CRY3_dark"

Here we approximate Figure 1.B from Banerjee et al. (2007).

    A_as_default()
    autoplot(CRYs.mspct$CRY2_dark)

    autoplot(CRYs.mspct[c("CRY2_dark", "CRY2_light")])

    autoplot(CRYs.mspct[c("CRY1_dark", "CRY1_light")])

    autoplot(CRYs.mspct["CRY3_dark"], range = c(300,700))

    ggplot(CRYs.mspct[c("CRY1_dark", "CRY2_dark", "CRY3_dark")]) +
      geom_line(aes(linetype = spct.idx)) +
      expand_limits(x = 300)

## Spectral absorbance of phototropins

    names(PHOTs.mspct)

    ## [1] "PHOT1_fluo"  "PHOT2_fluo"  "PHOT1_dark"  "PHOT1_light"

    autoplot(PHOTs.mspct[c("PHOT1_fluo", "PHOT2_fluo")]) +
      expand_limits(x = 300)

    autoplot(PHOTs.mspct[c("PHOT1_dark", "PHOT1_light")])

## UVR8 absorbance

    autoplot(UVR8s.mspct)

## Spectral absorbance of zeitloupe proteins

    names(ZTLs.mspct)

    ## [1] "ZTL_dark"  "ZTL_light"

    autoplot(ZTLs.mspct) +
      expand_limits(x = 300)

## Photosynthesis action spectra

    photon_as_default()

    names(McCree_photosynthesis.mspct)

    ## [1] "amaranth" "oats"

    autoplot(McCree_photosynthesis.mspct)

## Carotenoids

    A_as_default()

    names(carotenoids.mspct)

    ## [1] "beta_carotene"    "dihydro_lycopene" "lycopene"         "lutein"
    ## [5] "phytoene"         "phytofluene"      "violaxanthin"     "zeaxanthin"

    autoplot(carotenoids.mspct[1:4],
             annotations = c("-", "labels", "boxes"))

    autoplot(carotenoids.mspct[5:length(carotenoids.mspct)],
             annotations = c("-", "labels", "boxes"))

## Chlorophylls

    A_as_default()

    names(chlorophylls.mspct)

    ## [1] "Chl_a_MethOH" "Chl_a_DME"    "Chl_b_DME"

    autoplot(chlorophylls.mspct[c("Chl_a_DME", "Chl_b_DME")])

    autoplot(chlorophylls.mspct[c("Chl_a_DME", "Chl_a_MethOH")])

### Fluorescence

    names(chlorophylls_fluorescence.mspct)

    ## [1] "Chl_a_MethOH" "Chl_a_DME"    "Chl_b_DME"

    autoplot(chlorophylls_fluorescence.mspct[c("Chl_a_DME", "Chl_b_DME")])

    autoplot(chlorophylls_fluorescence.mspct[c("Chl_a_DME", "Chl_a_MethOH")])

## Optical properties of leaves

    Tfr_as_default()

    names(Solidago_altissima.mspct)

    ## [1] "lower_adax" "lower_abax" "upper_adax" "upper_abax"

    autoplot(Solidago_altissima.mspct$lower_adax)

    autoplot(Solidago_altissima.mspct$lower_abax)

    autoplot(as.filter_mspct(Betula_ermanii.mspct))

    autoplot(as.reflector_mspct(Betula_ermanii.mspct))

## Fluorescence of leaves

    names(leaf_fluorescence.mspct)

    ## [1] "wheat_Fo_ex355nm"

    autoplot(leaf_fluorescence.mspct$wheat_Fo_ex355nm)

## Water vapour in air

The functions described in this section and the following one have been migrated from package ‘photobiology’ (>= 0.12.0) to ‘photobiologyPlants’ (>= 0.6.0).

Water vapour partial pressure in air depends on temperature and on whether air is in equilibrium with liquid water or ice.Not considered here, solutes in water and surface interactions also affect the equilibrium. The examples below use the default equation for the computation of saturated water vapour pressure. The default is Tetens’ equation from 1930. Currently supported methods are `"tetens"`, modified `"magnus"`, `"wexler"` and `"goff.gratch"`.

    water_vp_sat(20) # temperature in C, partial pressure in Pa

    ## [1] 2338.023

    water_vp_sat(20) * 1e-3 # temperature in C, partial pressure in kPa

    ## [1] 2.338023

    vp_sat.df <- data.frame(temperature = -20:100,
                            vp.sat = c(water_vp_sat(-20:-1, over.ice = TRUE),
                                       water_vp_sat(0:100)) * 1e-3)

    ggplot(vp_sat.df, aes(temperature, vp.sat)) +
      geom_line() +
      labs(x = "Temperature (C)", y = "Water valour pressure at saturation (kPa)")

Conversion of water vapour pressure to relative humidity and vice versa is based on the curve shown in the figure above.

    water_vp2RH(1000, 25) # Pa and C -> RH%

    ## [1] 31.57191

    water_vp2mvc(1000, 25) # Pa and C ->  mass per volume g m-3

    ## [1] 7.264556

The reverse conversion functions are `water_RH2vp()`, `water_mvc2vp()`.

If we know the actual vapour pressure we can compute at which temperature this pressure would the saturating (RH = 100%), or dew point.

    water_dp(1000) # Pa -> C

    ## [1] 6.973856

If the vapour pressure is very low, instead of dew point we have to compute the freezing point.

    water_fp(500) # Pa -> C

    ## [1] -2.40697

Function `water_vp_sat_slope()` can be used to compute the slope of the curve in the figure above as a function of air temperature, and function `psychrometric_constant()` to compute the psychrometric constant as a function of air temperature.

## Reference evapotranspiration

Evapotranspiration is the combined water fluxes between a vegetation canopy and the atmosphere, It is the sum of transpiration (water that evaporates inside leaves and flows through stomata) and evaporation (water that evaporated from the soil and other surfaces, including from the wet outer surfaces of plants and their leaves). Measured evapotranspiration is described as actual evapotranspiration (\(\mathrm{ET}\)), the maximum rate of evapotranspiration of short vegetation canopy is called reference evapotranspiration (\(\mathrm{ET}_\mathrm{ref}\)), also described as potential evapotranspiration (\(\mathrm{PET}\))). Potential evapotranspiration can be measured on irrigated vegetation, but can also be estimated from meteorological conditions. Supported methods are the current FAO recommended and some earlier ones still in use.

Instantaneous \(\mathrm{ET}_\mathrm{ref}\) expressed in \(mm\ h^{-1}\) can be obtained with `ET_ref()`.

    ET_ref(temperature = 20, # C
           water.vp = water_RH2vp(relative.humidity = 70, # RH%
                                  temperature = 20), # C -> Pa
           wind.speed = 0, # m s-1
           net.irradiance = 100) # W m-2

    ## [1] 0.172792

Daily \(\mathrm{ET}_\mathrm{ref}\) expressed in \(mm\ d^{-1}\) can be obtained with `ET_ref_day()`

    ET_ref_day(temperature = 20, # C daily mean
               water.vp = 1636.616, # Pa daily mean
               wind.speed = 5, # m s-1 daily mean
               net.radiation = 15e6) # 15 MJ / d / m2 daily total !

    ## [1] 7.199597

As many of other factions in the package, these functions are vectorized.

    ET_ref(temperature = 20, # C
           water.vp = water_RH2vp(relative.humidity = (1:9) * 10, # RH%
                                  temperature = 20), # C -> Pa
           wind.speed = 5, # m s-1
           net.irradiance = 10) # W m-2

    ## [1] 0.01733964 0.01733277 0.01732590 0.01731904 0.01731217 0.01730530 0.01729843
    ## [8] 0.01729157 0.01728470

Potential evapotranspiration is in most situation proportional to the available radiant energy.

    ET_ref_irrad.df <-
      data.frame(irrad = (1:40) * 10,
                 ET.ref = ET_ref(temperature = 20, # C
                                 water.vp = water_RH2vp(relative.humidity = 70, # RH%
                                                        temperature = 20), # C -> Pa
                                 wind.speed = 5, # m s-1
                                 net.irradiance = (1:40) * 10) # W m-2
      )
    ggplot(ET_ref_irrad.df, aes(irrad, ET.ref)) +
      geom_line() +
      labs(x = expression("Global radiation "*(W~m^{-2})),
           y = expression("Reference evapotranspiration "*(mm~h^{-1})))

Function `net_irradiance()` simplifies the computation of net irradiance, needed as input for the computation of reference evapotranspiration.